About the real Waring rank of polynomials and their geometry = 다항식들의 실수 와링 랭크와 그 기하에 대하여

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The Waring rank of the given polynomial is the minimal number of linear forms whose sum of powers is equal to the polynomial. We study real ternary and quaternary forms whose real rank equals the generic complex rank,and we characterize the semialgebraic set of sums of powers representations with that rank. Complete results are obtained for ternary quadrics and cubics. For ternary quintics and quaternary cubic we determine the real rank boundary.For ternary quartics, sextics and septics we identify some of the components of the real rank boundary. The real varieties of sums of powers are stratified by discriminants that are derived from hyperdeterminants. For the quaternary case, we also obtain complete results for quadrics and cubics, and partial results for quartics. Also we present some algorithms to calculate the semialgebraic set of sums of powers and real rank boundaries.
Advisors
Kwak, Si Jongresearcher곽시종researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2017
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2017.8,[iii, 50 p. :]

Keywords

Algebraic geometry▼aWaring rank▼aTensor; 대수기하학▼a와링 랭크▼a텐서

URI
http://hdl.handle.net/10203/241911
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=718846&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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